Chief Dan Ghiorso said the cause of the fire remains unknown, but that it did not appear to be suspicious in nature.
The fire was reported at 1:31 a.m. and was quickly extinguished he said.
The Woodside Store museum at 330 Tripp Road is one of Woodside's most historic sites. The 1850 wooden structure, used as a general store, post office, and dental office during the town's lumber industry era, has been restored and displays goods used by the residents of the area at that time. It is part of the San Mateo County park system.